Q.State Faraday's laws of electromagnetic induction, both in words and as the single mathematical statement $\mathcal{E}=-N\dfrac{d\Phi_B}{dt}$. Explain what each symbol represents.

Faraday's laws state that a changing magnetic flux linked with a closed circuit induces an emf in it, with magnitude $|\mathcal{E}|=N\,d\Phi_B/dt$, or, including Lenz's law's direction as a minus sign, $\mathcal{E}=-N\,d\Phi_B/dt$. The induced emf exists only while the flux is actually changing, and only the RATE of change matters -- a small change happening quickly can induce a larger emf than a big change happening slowly. Flux can change because the field $B$ changes, the area $A$ changes, or the angle $\theta$ between them changes (equivalently, because a conductor moves through the field).